Prior art grips used with very small diameter (e.g., 10 to 50 microns) filaments have included grips with flat rubber gripping pad surfaces, such as the pneumatic grips sold by the assignee hereof, Instron Corporation, Canton, Mass., under the designation Model 2712, and the mechanically actuated grips sold by said assignee under the designation Model 2711. Such prior art grips have also included grips in which a fiber is wrapped around a conical "horn" and then pressed thereagainst, as in devices sold by said assignee under the designation Model 2714.